President Obama used part of his speech at Berlin’s historic Brandenburg Gate to return to the vision of reducing the role and number of nuclear weapons that he first articulated four years ago in Prague. In doing so, he outlined his arms control agenda for the remainder of his presidency. Let’s hope he makes progress. It would be good for U.S. and global security.

One year after his Prague speech, the president signed the New Strategic Arms Reduction Treaty (New START) with then-Russian President Medvedev. New START requires that the United States and Russia each reduce to no more than 1,550 deployed strategic warheads by 2018, and the sides currently are well along in implementing those cuts.

The president has issued new guidance regarding the employment of nuclear weapons. We won’t see that document, which is highly classified. But he told his audience in Germany that the United States could reduce its deployed strategic weapons further—by one-third below New START levels.

This is a logical next step in the process of moving U.S. and Russian strategic nuclear forces to lower and more reasonable levels 20 years after the end of the Cold War. It would cut the nuclear threat to the United States, offer the prospect of future defense budget savings, and bolster U.S. diplomatic efforts with third countries to increase the pressure on problem states such as Iran and North Korea.

Some wasted no time in criticizing the proposed reductions as undercutting U.S. security. That is difficult to see. Even with an arsenal reduced to some 1,000 deployed strategic warheads—plus several thousand reserve strategic and tactical weapons—the United States could easily maintain a robust, effective and credible nuclear deterrent. Can the critics explain what new danger would arise or what country would act differently toward the United States? Would Pyongyang adopt an aggressive new course if the U.S. military had only 300-400 times as many nuclear weapons as North Korea instead of 500 times?

The main question is whether President Putin will engage. Moscow publicly has shown little enthusiasm for further nuclear cuts, but the Russians may have incentives—such as saving money on their strategic forces—to deal. We’ll get a better sense of this when the two presidents meet in Russia in early September.

Mr. Obama also called for cuts in U.S. and Russian tactical nuclear weapons in Europe. It is high time for the nuclear superpowers to expand their discussion to include tactical weapons (and reserve strategic warheads as well). Getting the Russians to agree to talk about these will be hard, but Washington should press and not take nyet for an answer.

The president announced that he would extend the nuclear material security process that he launched in 2010. That brought together leaders of more than 40 countries to develop an action plan to ensure tight controls on stockpiles of highly-enriched uranium and plutonium in order to keep those essential components of nuclear bombs out of the hands of rogue states and terrorist groups. Significant progress has been made, but the president’s original four-year timeline was way too ambitious. Following next year’s meeting in the Netherlands, Mr. Obama will host another summit in 2016 to keep the nuclear security effort going.

The president stated that he would continue to work to build Senate support for ratification of the Comprehensive Test Ban Treaty. Gaining a two-thirds majority, particularly given the partisan nature of politics today, poses an enormous challenge. But ratification would serve the U.S. interest by bringing the treaty closer to entry into force.

The United States has built the capability to maintain confidence in the reliability of its nuclear arsenal without testing, and improved verification mechanisms mean that any militarily significant test would be detected. Moreover, Nevada fought tooth and nail against storage of nuclear waste at the former test site located 60 miles from Las Vegas; does anyone believe a resumption of testing would be feasible politically? Finally, the United States conducted more nuclear tests than the rest of the world combined and acquired a huge amount of data. Why let other countries have a chance to catch up?

Mr. Obama also reiterated his earlier calls for a treaty to end the production of highly-enriched uranium and plutonium. That would be an important action, though Pakistan so far has blocked consensus at the Conference on Disarmament on a mandate for such a negotiation. Perhaps it is time for Washington and other like-minded countries to explore an alternate venue for addressing this question.

When the president spoke in Prague in 2009, he laid out his ultimate vision of a world without nuclear weapons, albeit with a number of qualifiers. He mentioned that objective only in passing at the Brandenburg Gate, perhaps reflecting his understanding that, given the need to negotiate with other countries and Congress, achieving truly transformational nuclear reductions will be far more difficult than he might have hoped four years ago. He nevertheless laid out in Berlin a sensible agenda to move us toward a more secure nuclear future for the United States and the world.